C5.ω is obtained by adding, schematically, to the strict-implicational fragment C5 of S5 the axiom → ) → . This paper presents a fully general proof that neither C5.ω nor any of a descending chain of its extensions is complete with respect to any class of frames, correcting the garbled details of a version skeched in an earlier paper , 201-208).

A four-valued matrix is presented which validates all theorems of the implicational fragment, IF, of the classical sentential calculus in which at most two distinct sentence letters occur. The Wajsberg/Diamond-McKinsley Theorem for IF follows as a corollary: every complete set of axioms (with substitution and detachment as rules) must include at least one containing occurrences of three or more distinct sentence letters. Additionally, the matrix validates all IF theses built from nine or fewer occurrences of connectives and letters. So the (...) classic result of Jagkovski for the full sentential calculus -that every complete axiom set must contain either two axioms of length at least nine or else one of length at least eleven-can be improved in the implicational case: every complete axiom set for IF must contain at least one axiom eleven or more characters long. Both results are "best possible", and both apply as well to most subsystems of IF, e.g., the implicational fragments of the standard relevance logics, modal logics, the relatives of implicational intutionism, and logics in the Lukasiewicz family. (shrink)

detail a question that, for a quarter of a century, remained open despite intense study by various researchers. Is the formula XC B = e(x e(e(e( ) e( )) z)) a single axiom for the classical equivalential calculus when the rules of inference consist..

Morality and economic rationality: integrative economic ethics as the rational ethics of economic activity; Part II. Reflections on the Foundations of Economic ...

In this new book, Ulrich Beck develops his now widely used concepts of second modernity, risk society and reflexive sociology into a radical new sociological ...

By assembling authors with a wide range of different disciplinary backgrounds, from philosophy, literature, political science, sociology to medical anthropology ...

At the beginning of the 21st century the conditio humana cannot be understood nationally or locally but only globally. This constitutes a revolution in the social sciences. The `sociological imagination' so far has basically been a nation state imagination. The main problem is how to redefine the sociological frame of reference in the horizon of a cosmopolitan imagination. For the purpose of empirical research I distinguish between three concepts: interconnectedness, liquid modernity and cosmopolitization from within. The latter is a kind (...) of class analysis after class analysis, which takes on board globalization internalized. For the purposes of social analysis, therefore, it is necessary to distinguish systematically between the national manifestation on the one hand and cosmopolitan reality of `global flows', currents of information, symbols, money, risks, people, social inequalities, on the other. This internal involuntary and often unseen cosmopolitanization from below of the national sphere of experience is occurring, however, with the power of economic globalization. So what does inner `cosmopolitanization' mean? The key concepts and questions of a way of life, such as nourishment, production, identity, fear, memory, pleasure, fate, power and politics, can no longer be located and understood nationally, but only globally whether in the shape of globally shared collective futures, capital flows, impending ecological or economic catastrophes, global foodstuff chains, transnational power games, or the `Esperanto' of pop music. In this article I look at transformation in the understanding of space-time, of identity, of the production paradigms, as well as at the resulting consequences for key sociological concepts like class and power and, within this frame, point to certain dilemmas of cosmopolitanism. (shrink)

How can one distinguish the concept of second modernity from the concept of postmodernity? Postmodernists are interested in deconstruction without reconstruction, second modernity is about deconstruction and reconstruction. Social sciences need to construct new concepts to understand the world dynamics at the beginning of the 21st century. Modernity has not vanished, we are not post it. Radical social change has always been part of modernity. What is new is that modernity has begun to modernize its own foundations. This is what (...) it means to say modernity has become reflexive. It has become directed at itself. This causes huge new problems both in reality and in theory. There has been a pluralization of the boundaries within and between societies, between society and nature, between Us and Other, between life and death. This pluralization also changes the inherent nature of boundaries. They become not so much boundaries as a variety of attempts to draw of boundaries. Border conflicts become transformed into conflicts over the drawing of boundaries. Where postmodernism simply celebrates this multiplication of boundaries, the theory of second modernity starts with the problem this new reality poses for individual and collective decisions, and with the problem that the continued existence of such decisions poses for theory. Institutions that are capable of such conscious boundary drawing are enabled in a way that those of the first modernity were not. But this process also generates qualitatively new kinds of trouble and crises. To investigate those troubles is to unveil the emergence of the second modernity. (shrink)

Epistemic arguments play a significant role in the foundations of market liberalism as exemplified, in particular, by the work of F. A. Hayek. Competition in free markets is claimed to be the most effective device both to utilize the knowledge dispersed throughout society as well as create new knowledge through innovation competition. The fast pace with which new economic opportunities are discovered and costs are reduced is considered proof of the benefits of free markets to the common good. However, with (...) its inherently unpredictable consequences, innovation competition is actually ambiguous in this respect. This feature raises questions over the stringency of market liberal pleas that oppose quests for redistribution and environmental concerns in an absolute fashion. (shrink)